Perhaps, we can't really know for sure what would have happened; what we do know though, is that your destruction of the heart definitely served as a catalyst to Morrowind's problems.
Honestly, I always got the impression that, even though he wanted to be the sole controller of the Heart, Dagoth Ur seemed like he wanted folks to like him (He was awfully polite
). That said, I could see him using his ill-gotten gains to keep the Moon aloft when Vivec failed to do so simply as a means of showing the Dunmer that -he- was the one they should be worshipping, not the Tribunal.
That too, though, is speculation.